[HOW-TO] - Solved! “This device isn’t eligible for the requested build” Error in iTunes When Updating iOS 6.1

Mac OS X:
Step 1. On your Mac, go to your “Applications” folder.
Step 2. Now navigate to the “Utilities” folder.
Step 3. Launch “Terminal”.
Step 4. Type “sudo nano /etc/hosts” (without quotes) and hit return.
Step 5. Enter your password
Step 6. Use the down arrow key to find the “gs.apple.com” entries. Once the cursor is in front, make sure you comment out the line(s) by entering “#” in front of the text.
Step 7. Save the file by pressing CONTROL+O.
Step 8. Exit the nano editor by pressing CONTROL+X.
Step 9. Restore your iDevice.

Windows:
Step 1. Start --> Programs --> Accessories
Step 2. Run Notepad or WordPad 

Step 3. Click “Open..” from File menu.
Step 4. Browse to Windows/System32/drivers/etc 

Step 5. In “files of type:” select all documents
Step 6. Open “hosts”
Step 7. Delete all line that has “gs.apple.com” or something like that 

Step 8. Hit Save
Step 9. Restore your device